Two relaxed inertial forward-backward-forward algorithms for solving monotone inclusions and an application to compressed sensing

Two novel algorithms, which incorporate inertial terms and relaxation effects, are introduced to tackle a monotone inclusion problem. The weak and strong convergence of the algorithms are obtained under certain conditions, and the R-linear convergence for the first algorithm is demonstrated if the set-valued operator involved is strongly monotone in real Hilbert spaces. The proposed algorithms are applied to signal recovery problems and demonstrate improved performance compared to existing algorithms in the literature.